Question

Find the value of x and y for function, y = x³ + 21 where, the rate of change ofy is three times as the rate of change of x.

Answer 1

Given, function y = x³ + 21

Diff w.r.t. t,
dy/dx = 3x² (dx/dt)…..(i)

According to question

dx/dt = 3(dx/dt) …..(ii)

From equation (i) and (ii)

3x² = 3

⇒ x = ± 1

In equation y = x³ + 21

Putting x = 1

y = 1³ + 21

= 1 + 21 =22

Putting x = -1

y = (- 1)³ + 21 = -1 + 21 = 20

So, x = ± 1 and y = 22, 20